Why is it better to use a lead controller than a PD controller?

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The lead controller helps us in two ways: it can increase the gain of the open loop transfer function, and also the phase margin in a certain frequency range. But why could we not use just a PD controller, that increases the phase over a wider range of frequencies?

The use of the derivative action should always be limited: it helps improve the control performance when the error signal changes rapidly, but for the same reason it could amplify unwanted disturbances on the measured output.